Adaptive Incentive Design with Regret Minimization

TL;DR

This paper presents RAID, an adaptive incentive design algorithm that minimizes regret under information asymmetry by combining exploration and exploitation, with relaxed excitation conditions and proven asymptotic optimality.

Contribution

It introduces the RAID algorithm with a novel estimator that relaxes excitation assumptions and guarantees asymptotic regret minimization in incentive design.

Findings

RAID algorithm achieves asymptotic regret minimization.

The estimator is strongly consistent under weaker excitation conditions.

Numerical experiments demonstrate convergence rates.

Abstract

Incentive design constitutes a foundational paradigm for influencing the behavior of strategic agents, wherein a system planner (principal) publicly commits to an incentive mechanism designed to align individual objectives with collective social welfare. This paper introduces the Regret-Minimizing Adaptive Incentive Design (RAID) problem, which aims to synthesize incentive laws under information asymmetry and achieve asymptotically minimal regret compared to an oracle with full information. To this end, we develop the RAID algorithm, which employs a switching policy alternating between probing (exploration) and estimate-based incentivization (exploitation). The associated type estimator relies only on a weaker excitation condition required for strong consistency in least squares estimation, substantially relaxing the persistence-of-excitation assumptions previously used in adaptive incentive design. In addition, we establish the strong consistency of the proposed type estimator and prove that the incentive obtained asymptotically minimizes the planner's average regret almost surely. Numerical experiments illustrate the convergence rate of the proposed methodology.